An N-dimensional version of the Beurling-Ahlfors extension

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Kovalev, Leonid V.
Onninen, Jani
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Abstract
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We extend monotone quasiconformal mappings from dimension n to n+1 while preserving both monotonicity and quasiconformality. The extension is given explicitly by an integral operator. In the case n=1 it yields a refinement of the Beurling-Ahlfors extension.
Comment: 9 pages. Added references, edited concluding remarks
Keywords
Mathematics - Complex Variables, 30C65, 47H05, 47B34
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